"I'm not contemplating any of that," Emanuel responded. "I'm not delving into that conversation with you."

The former Apprentice host remains the frontrunner for the Republican presidential nomination, while Emanuel and Whitesell are Democrats who have donated to Hillary Clinton's 2016 campaign. In September, Trump sold the Miss Universe Organization to WME|IMG, whose portfolio includes IMG Models as well as 32 Fashion Weeks around the world, days after purchasing NBC's half of the company.

Elsewhere in politics, Emanuel said that he would be happy to be "the first one in line" to help arrange a post-presidency book or speaking tour for Barack Obama, but noted that the commander-in-chief is likely to take a break after stepping down, "having heard from my brother [Rahm Emanuel, mayor of Chicago and Obama's former chief of staff] what happens with other presidents."

"I think it's contingent on whom she faces," he added, although when asked about a Trump-Clinton scenario, he cut the line of questioning short: "I can give you my brother's number, he'll be happy to [talk]. I don't want him to talk about Hollywood, and I don't want to talk about political issues."